Problem: Rewrite as a simplified fraction. ${1.7\overline{38} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1738.3838...\\ 10x &= 17.3838...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1721}$ ${x = \dfrac{1721}{990}} \text{or} {1 \dfrac{731}{990}}$